The proper motion of features in the pc-scale jet has been measured
directly implying a value
0.5c h-1 for the projected
jet velocity. Whether this is simply a pattern speed or
the true flow velocity is still unknown, as is the inclination angle with
respect to the sky plane. Estimates of the velocity of
the jet on kpc-scales are even more problematic, but there are a few indirect
methods that have been used, which we review. In this section we assume
h = 0.75, both for simplicity, and because the calculations are at
best order-of-magnitude.

Estimating is
difficult. It has been suggested that jet
shocks are very efficient at converting bulk kinetic energy into
relativistic particles
(Axford, Leer, and
McKenzie 1982,
Bell 1987).
At the minimum the jet must also do work to expand the ambient medium: work
PL x
VL 1059 ergs,
where PL = lobe pressure = 8 x 10-11 dyn
cm-2, and
VL = 7 x 1068 cm3. Dividing this by the source
lifetime of ts
106.8 yrs (as estimated from
synchrotron spectral ageing arguments; see below) yields
5 x 1044 ergs sec-1, thereby setting a very rough upper
limit: 0.4. In reality,
is likely to be
considerably less than this
(Dreher 1985,
Leahy 1991),
in particular if
the lobe pressures are substantially different than dictated by minimum
energy.

One can also consider the total mass flux in the jet and the upper limit
to the mass in the radio lobes, ML, to derive a jet velocity:
vj = ts x PHS x AHS /
ML. Using a lobe density < 2 x 10-4
cm-3 derived
from the lack of internal Faraday dispersion
(Dreher et al. 1987)
implies ML < 2.4 x 1041 gm. The lower limit to the jet
velocity is then 0.01 c.

Both of the above calculations are invalid in the case of departure from
minimum energy conditions, or a time-variable energy (or mass) supply in
the jet. The mass estimate also depends on the assumptions of magnetic
field strength and geometry inherent in the internal Faraday
depolarization calculation.

Williams (1991)
develops a simple hydrodynamic model relating observable
parameters such as the ratio of jet width to lobe width and the ratio of
hotspot pressure to lobe pressure to physical parameters such as the
jet Mach number and ambient-to-jet density contrast. Applying this
model to Cygnus A he finds Mj 8, and
2 x 10-4 for a Newtonian ideal fluid. He then balances jet ram
pressure against minimum pressures in the hotspots and finds a required
jet velocity somewhat greater than the speed of light. Williams uses
this result to argue that the jet must be relativistic on kpc-scales,
and must be composed primarily of a relativistic (pair) plasma.
However, his calculations apply to axisymmetric flows in a constant
density medium. Including jets which vary direction on short
timescales, and/or density gradients in the ambient medium, would widen
the lobes over the axisymmetric case, and invalidate the above
arguments.

Muxlow, Pelletier, and
Roland (1988)
and Carilli et al. (1991a)
have used the observed spectra of the Cygnus A radio hotspots to constrain
various physical parameters of the jet. Their basic conclusion is that
the various `features' in the hotspot spectra are consistent with a
model involving particle acceleration at a strong shock in a Newtonian
fluid with a mildly relativistic jet velocity
( 0.4 c).

Roland and Hermsen (1995)
develop a two-component model for the jets in
extragalactic radio sources involving a narrow `core' jet consisting of
a pair-plasma, and moving at
c, sheathed by a classical
(proton-electron) plasma moving trans-relativistically
( 0.7c).
The relativistic jet component gives rise to the large Lorentz factors,
and ray emission,
from superluminal radio jets, while the
classical component dominates the dynamics, and gives rise to the large
scale radio emitting structures (lobes, hotspots, etc...).

Overall, there are no data which necessitate a highly relativistic jet
on kpc-scales or a jet consisting of only pair plasma
(Begelman et al. 1984)
in Cygnus A. On the other hand, neither of these is
currently precluded, emphasizing our current ignorance of the real
physical conditions in jets. Mildly relativistic flow would be
consistent with the observed jet-to-counterjet surface brightness
ratio, as discussed below.